Geometry

On Surface Measures on Convex Bodies and Generalizations of Known Tangential Identities

Authors: Johan Aspegren
Comments: 12 Pages.

One theme of this paper is to extend known results from polygons and balls to the general convex bodies in n− dimensions. An another theme stems from approximating a convex surface with polytope surface. Our result gives a sufficient and necessary condition for an natural approximation method to succeed (in principle) in the case of surfaces of convex bodies. Thus, Schwartz`s paradox does not affect our method. This allows us to denefine certain surface measures on surfaces of convex bodies in a novel and simple way.
Category: Geometry